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<h1><font color="#FF0000">Pill Box Cavity</font></h1>

<dl>
  <dd>There are two cavities in <span lang="en-ca">PTC</span>: a standard pill box and a traveling wave 
cavity. Here we are dealing with the pill box.</dd>
  <dd>&nbsp;</dd>
  <dd>In PTC the time of flight (or path length) is properly computed inside the 
cavity. The following parameter has been added to the C_ structure:</dd>
  <dd>&nbsp;</dd>
  <dd><font color="#FF0000"><u><b><font size="5">1) C_%CAVITY_TOTALPATH</font><font size="5"> 
  = 1 ==&gt; </font><font color="#000080">Done Correctly</font><font color="#FF0000">
  </font></font></b></u> </dd>
  <dt>&nbsp;</dt>
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    <dt><img border="0" src="exact.jpg" width="398" height="460"></dt>
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    <dd>
    <p align="left">&nbsp;</dd>
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<p>C_%CAVITY_TOTALPATH = 1 implies (see the code) that the global variable 
TOTALPATH is set locally to 1 even if the TOTALPATH = 0.&nbsp; This is necessary 
for a correct cavity treatment. </p>

<p>I read Dr. Kapin's note. PTC does exactly that. If TIME=false and an infinite 
number of steps is used, I think the results should agree with Kapin's formula. 
Of course in PTC one can use TIME=true (as in SixTrack) and then the formula for 
T<sub>g</sub> is different. </p>

<p><u><font color="#FF0000"><b><font size="5">2) C_%CAVITY_TOTALPATH = 0 ==&gt;
</font></b></font><b><font size="5"><font color="#000080">Done Incorrectly on 
purpose</font></font></b></u></p>
<p>Sometimes we want to put a cavity with a length because in the real machine 
it does. We also do not want to be bothered with refitting the cavity to achieve 
ideal behavior. In that case, we can set C_%CAVITY_TOTALPATH = 0.</p>
<p>This means that in the cavity, relative time is always used. I makes the pill 
box cavity a little like a traveling wave cavity: a particle which arrives on 
the crest at s=0 stays on the crest. Therefore (0,0,0,0,0,0) is sent to itself 
if Totalpath=0</p>
<p>This option is useful if one does not want to be bothered.</p>
<p><b><font color="#008000" size="5"><u>3) Other options:</u></font></b></p>
<p><font color="#FF0000">N_BESSEL&gt;0 </font>then Maxwell's equation is solved in 
the body up to degree N_BESSEL. This is the famous J<sub>0</sub> term in the 
cavity.</p>
<p>Finally, fringe field effect can be turned on in the usual manner either 
permanently or through the global state FRINGE.</p>
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